On Bidding with Securities: Risk Aversion and Positive Dependence

TL;DR

This paper extends the analysis of auction revenue rankings based on securities to risk-averse bidders and different dependence assumptions, showing conditions under which revenue comparisons hold.

Contribution

It generalizes previous results by demonstrating how risk aversion and positive dependence affect revenue rankings in auctions with securities.

Findings

Steeper securities yield higher expected revenue under risk neutrality.

Revenue ranking holds for risk-averse bidders in second price auctions.

Relaxing affiliation to FOSD alters the revenue comparison outcomes.

Abstract

DeMarzo et al. (2005) consider auctions in which bids are selected from a completely ordered family of securities whose values are tied to the resource being auctioned. The paper defines a notion of relative steepness of families of securities and shows that a steeper family provides greater expected revenue to the seller. Two assumptions are: the buyers are risk-neutral; the random variables through which values and signals of the buyers are realized are affiliated. We show that this revenue ranking holds for the second price auction in the case of risk-aversion. However, it does not hold if affiliation is relaxed to a less restrictive form of positive dependence, namely first order stochastic dominance (FOSD). We define the relative strong steepness of families of securities and show that it provides a necessary and sufficient condition for comparing two families in the FOSD case. All results extend to the English auction.